Problem: A circle has a circumference of ${12}$. It has an arc of length $\dfrac{8}{5}$. What is the central angle of the arc, in degrees?
The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{\theta}}{360^\circ} = {\dfrac{8}{5}} \div {12}$ $\dfrac{{\theta}}{360^\circ} = \dfrac{2}{15}$ ${\theta} = \dfrac{2}{15} \times 360^\circ$ ${\theta} = 48^\circ$ ${12}$ ${\dfrac{8}{5}}$ ${48^\circ}$